On a mixed nonlocal problem for a wave equation.
On a mixed problem for a constant coefficient second-order system.
On a mixed problem for a coupled nonlinear system.
On a mixed problem for a linear coupled system with variable coefficients.
On a Model of Leukemia Development with a Spatial Cell Distribution
In this paper we propose a mathematical model to describe the evolution of leukemia in the bone marrow. The model is based on a reaction-diffusion system of equations in a porous medium. We show the existence of two stationary solutions, one of them corresponds to the normal case and another one to the pathological case. The leukemic state appears as a result of a bifurcation when the normal state loses its stability. The critical conditions of leukemia development are determined by the proliferation...
On a model of rotating superfluids
We consider an energy-functional describing rotating superfluids at a rotating velocity , and prove similar results as for the Ginzburg-Landau functional of superconductivity: mainly the existence of branches of solutions with vortices, the existence of a critical above which energy-minimizers have vortices, evaluations of the minimal energy as a function of , and the derivation of a limiting free-boundary problem.
On a model of rotating superfluids
We consider an energy-functional describing rotating superfluids at a rotating velocity ω, and prove similar results as for the Ginzburg-Landau functional of superconductivity: mainly the existence of branches of solutions with vortices, the existence of a critical ω above which energy-minimizers have vortices, evaluations of the minimal energy as a function of ω, and the derivation of a limiting free-boundary problem.
On a model system for the oblique interaction of internal gravity waves
On a model system for the oblique interaction of internal gravity waves
We give local and global well-posedness results for a system of two Kadomtsev-Petviashvili (KP) equations derived by R. Grimshaw and Y. Zhu to model the oblique interaction of weakly nonlinear, two dimensional, long internal waves in shallow fluids. We also prove a smoothing effect for the amplitudes of the interacting waves. We use the Fourier transform restriction norms introduced by J. Bourgain and the Strichartz estimates for the linear KP group. Finally we extend the result of [3] for lower...
On a monodromy group and irreducibility conditions of a fourth order Fuchsian differential system of Okubo type.
On a motion of a ball in a viscous fluid. (Zur Bewegung einer Kugel in einer zähen Flüssigkeit.)
On a multilevel Krylov method for the Helmholtz equation preconditioned by shifted Laplacian.
On a Navier-Stokes type equation and inequality
A Navier-Stokes type equation corresponding to a non-linear relationship between the stress tensor and the velocity deformation tensor is studied and existence and uniqueness theorems for the solution, in the 3-dimensional case, of the Cauchy-Dirichlet problem, for a bounded solution and for an almost periodic solution are given. An inequality which in some sense is the limit of the equation is also considered and existence theorems for the solution of the Cauchy-Dirichlet problems and for a periodic...
On a necessary and sufficient condition for a blowing up of a solution to a mixed boundary problem for a certain nonlinear equation of Sobolev type.
On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation.
On a new class of generalized solutions for the Stokes equations in exterior domains
On a new superposition principle for optimization problem
On a non linear partial differential equation having natural growth terms and unbounded solution
On a non-homogeneous shallow-water problem
On a nonlinear boundary value problem of higher order